The Never-ending Series

In order to produce the next number in the series, we take the current number, square it, and then add up the digits. This becomes the next term in the sequence.

Starting with 11 as the 1st term, what is the 2008th term in this sequence?

Answer

The answer is 13.

The first few work out like so:

11, (121) 4, (16) 7, (49) 13, (169) 16, (256) 13....

After the first few, it will jump back and forth between 16 and 13. Seeing how 13 is our 4th term, 16 is our 5th, logic says that 13 will be our 2008th term since it repeats on every even nth term.Hide